261597 ÷ 41 
We're looking to find how many times 41 goes into 261597.

Moving on to step 1:
If we divide 2 by 41, we get 0 and a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 41

Step 2:
26 divided by 41 is 0 with a remainder of 26.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 26, we get 26.
Include the next digit (1) from the dividend after 26, then repeat: 261 / 41

Advancing to step 3:
41 goes into 261 6 times with a remainder of 15.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 246 from 261 and we're left with 15.
Append the next digit (5) from the dividend to 15 and continue with: 155 / 41

Step 4:
41 goes into 155 3 times with a remainder of 32.
Use 3 as the next digit of our solution. 
Result so far: 63.0
Subtract 123 from 155 to get 32.
Bring next digit (9) of the dividend behind the 32 and repeat the process: 329 / 41

Let's proceed to step 5:
The number 41 fits into 329 8 times, leaving a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 638.0
The remainder is 1 after subtracting 328 from 329.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 41

Advancing to step 6:
17 divided by 41 is 0 with a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 6380.0
The remainder is 17 after subtracting 0 from 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 7:
41 goes into 170 4 times with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 6380.4
If we subtract 164 from 170, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 8:
41 goes into 60 1 times with a remainder of 19.
Use 1 as the next digit of our solution. 
Result so far: 6380.41
The remainder is 19 after subtracting 41 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 9:
190 divided by 41 is 4 with a remainder of 26.
Write down 4 as next digit of the result. 
Result so far: 6380.414
If we subtract 164 from 190, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 10:
The number 41 fits into 260 6 times, leaving a remainder of 14.
The number 6 becomes the next digit in our result. 
Result so far: 6380.4146
If we take 246 away from 260, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 11:
140 divided by 41 is 3 with a remainder of 17.
Use 3 as the next digit of our solution. 
Result so far: 6380.41463
If we subtract 123 from 140, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 12:
The number 41 fits into 170 4 times, leaving a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 6380.414634
The remainder is 6 after subtracting 164 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
41 can be fit into 60 1 times, resulting in a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 6380.4146341
The remainder is 19 after subtracting 41 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 14:
If we divide 190 by 41, we get 4 and a remainder of 26.
The number 4 becomes the next digit in our result. 
Result so far: 6380.41463414
The remainder is 26 after subtracting 164 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Our division results in 6380.41463414 with a remaining 2.6e-08.